From orthodox wiki:
Traditional Christianity affirms that the laws or Torah of the Old Testament is the word of God, though many Christians deny that all of the laws of the Pentateuch apply directly to themselves as Christians. The New Testament indicates that Jesus Christ established a new covenent relationship between God and his people (Hebrews 8; Jeremiah 31:31-34) and this makes the Mosaic covenant in some senses obsolete (Hebrews 8:13). A change of covenant can imply a change of law. Many have interpreted Mark's statement, "thus he declared all foods clean" (Mark 7:19) to mean that Jesus taught that the pentateuchal food laws were no longer applicable to His followers. The writer of Hebrews indicates that the sacrifices and the Levitical priesthood foreshadowed Jesus Christ's offering of himself as the sacrifice for sin on the Cross and many have interpreted this to mean that once the reality of Christ has come, the shadows of the ritual laws cease to be obligatory (Heb 8:5; 9:23-26; 10:1). On the other hand, the New Testament repeats and applies to Christians a number of Old Testament laws, including "Love your neighbor as yourself" (Leviticus 19:18; compare the Golden Rule), "Love the LORD your God with all your heart, soul and strength" (Deuteronomy 6:4, the Shema) as well as every commandment of the Decalogue or Ten Commandments (Exod 20:1-17). In fact, in Matthew 5:17, Jesus said that He did not come to abolish the Law.
While some Christians from time to time have deduced from statements about the law in the writings of the apostle Paul that Christians are under grace to the exclusion of all law (see antinomianism), this is not the usual viewpoint of Christians.An example of one more common approach is found in the Westminster Confession of Faith (1646) which divides the Mosaic laws into three categories: moral, civil, and ceremonial. In the view of the Westminster divines, only the moral law such as most of the Ten Commandments directly applies to Christians today. Others limit the application of the Mosaic laws to those commands repeated in the New Testament. In the 1970s and 1980s a movement known as Christian Reconstructionism (Theonomy) argued that the civil laws as well as the moral laws should be applied in today's society as part of establishing a modern, theocratic state. Others are content to grant that none of the Mosaic laws apply as such and that the penalties attached to the laws were limited to the particular historical and theological setting of the Old Testament, and yet still seek to find moral and religious principles applicable for today in all parts of the law. The topic of Paul and the law is still frequently debated among New Testament scholars.
In the late 20th century some Christian groups, primarily those found in or influenced by Messianic Judaism, have asserted that Torah laws should be followed by Christians. Due to a different understanding of Biblical passages such as those referenced above, dietary laws, seventh day Sabbath, and Biblical festival days are observed in some way within such segments of Christianity. As with Orthodox Judaism, capital punishment and sacrifice are not practiced because there are strict Biblical conditions on how these are to be practiced. Christians who attempt to follow Torah law do not do such works in order to achieve salvation, but rather because they believe is it a way of more fully obeying God (see Sermon on the Mount and Matthew 5:17). See sources below (Lancaster and Berkowitz).